How many changes to a culture equal cultural suicide? Much of your argument seems to be built upon the premise that culture is a fixed thing or has some sort of essence that either survives from one generation to the next or doesn’t. Unfortunately, culture doesn’t have an essence. American culture today isn’t the same as it was in the 1950s. Differences become even greater when compared to the 1850s or the years immediately following the Revolutionary War. Wait a decade or two and we’ll see that it has changed significantly again, probably in ways that no one anticipated. Cultures evolve. Sometimes entire peoples do disappear for one reason or another, of course, but these examples are hardly applicable when talking about nations that still contain tens of millions of people and are not facing any imminent existential threat.
As for the birthrate jeopardizing our capacity to afford social programs like Social Security or healthcare, the US, as well as the world more generally, has plenty of money to fund these. The problem isn’t the volume of money in circulation or how many people are dividing it up between them. The problem is the money’s distribution. The US could, for example, easily eliminate or significantly raise the Social Security tax cap so that earnings greater than $132,900 (2019 cap) were subject to the tax. Approximately 3.5% of the population had incomes over $200,000 in 2017. This accounted for nearly 18% of all income earned in the United States. I haven’t taken the time to crunch the numbers, but it seems pretty obvious that by simply raising the income cap to around $500,000 or eliminating it entirely, Social Security could instantly increase its revenue stream by at least 10%. The same is true for Medicare. Crisis averted: No additional babies required.